Goran's parents met shortly after the end of World War II in Virovitica where his mother Borka lived and his father Franjo (who fought on the Partisan side during the war) attended a Yugoslav People's Army (JNA) military school.[3] Franjo Bregović soon got his first job, teaching ballistics at a Sarajevo military school, so the family (which at the time only had a daughter) moved there.[3] Goran, their second child, was born in 1950.

Goran was 10 years old when his parents divorced. In later interviews he mentioned his father's alcoholism as the reason for the breakdown of his parents' marriage.[3] Soon after the split, his father moved to Livno, taking Goran's younger brother Predrag with him while Goran remained living with his mother in Sarajevo, visiting his father and brother every summer in Livno.[3] Their father soon retired and eventually moved back to his home village in Zagorje while Goran's brother Predrag later moved back to Sarajevo for university studies.[3]

Goran played violin in a music school. However, deemed untalented, he was thrown out during second grade. His musical education was thus reduced to what his friend taught him until Goran's mother bought him his first guitar in his early teens. Bregović wanted to enroll in a fine arts high school, but his aunt told his mother that it was supposedly full of homosexuals, which precipitated his mother's decision to send him to a technical (traffic) school. As a compromise for not getting his way, she allowed him to grow his hair long. Upon entering high school, Goran joined the school band Izohipse where he began on bass guitar. Soon, however, he was kicked out of that school too (this time for misbehavior - he crashed into a school-owned Mercedes-Benz). Bregović then entered grammar school and its school band Beštije (again as a bass guitar player). When he was 16, his mother left him and moved to the coast, meaning that other than having a few relatives to rely on, he mostly had to take care of himself. He did that by playing folk music in a kafana in Konjic, working on construction sites, and selling newspapers.

Spotting him at a Beštije gig in 1969, Željko Bebek invited 18-year-old Bregović to play bass guitar in his band Kodeksi, which Goran gladly accepted.

Eventually, Kodeksi shifted setup so Bregović moved from bass to lead guitar, resulting in Kodeksi having the following line-up during summer 1970: Goran Bregović, Željko Bebek, Zoran Redžić and Milić Vukašinović. All of them would eventually become members of Bijelo Dugme at some point in the future. At the time, they were largely influenced by Led Zeppelin and Black Sabbath. During the fall of 1970, this resulted in departure of Željko Bebek, who (both as rhythm guitar player and singer) got phased out of the band. At the end of the year, Goran's mother and Zoran's brother arrived in Naples and took them back to Sarajevo.

Then, in the autumn of 1971, Goran enrolled at the University of Sarajevo's Faculty of Philosophy, studying philosophy and sociology. He soon quit, however. At the same time, Milić Vukašinović left for London, so Bregović formed a band with Nuno Arnautalić called Jutro (Morning), which Redžić soon joined as well. Over the next few years, the band changed lineups frequently, and on 1 January 1974 modified its name to Bijelo Dugme ("White Button").

At the time Bijelo Dugme was falling apart, Goran entered the world of film music. His first project was Emir Kusturica's Time of the Gypsies (1989). This turned out to be a great success (both the film and the soundtrack). Goran and Emir's collaboration continued, and Goran composed music (which was performed by Iggy Pop) for Emir's next film Arizona Dream (1993). During the war in Bosnia and Herzegovina, Goran lived in Paris, but he also lived in Belgrade. His next major project, music for Patrice Chéreau's Queen Margot was a great success as well, and as a result, the film won two awards on the 1994 Cannes Film Festival. The next year's Golden Palm award went to Underground, for which Goran Bregović composed the music.

In 1997, he worked with Turkish singer Sezen Aksu on her album Düğün ve Cenaze (Wedding and Funeral). After that album, he continued making composite albums with other musicians that were based on his music and singers' lyrics.

For many years Bregović performed with a large ensemble of musicians: a brass band, bagpipes, a string ensemble, a tuxedo-clad all-male choir from Belgrade, women wearing traditional Bulgarian costumes, and Roma singers make up his 40-piece band and orchestra.

Since 1998, and until about 2012, Bregović has been performing his music mainly in the form of concerts all over the world with his Weddings and Funerals Orchestra. This consists of 10 people (in the small version) or 37 (in the large version, although, in some instances, this number varies, depending on participants from the host country).

Since 2012 the orchestra consists of 9 people (in the small version) or 19 (in the large version), as it played in New York at the Lincoln Center on 15 July and 16 July 2016.[5]

In 2013, as part of his Asia-Pacific tour (including Australia, New Zealand, and Hong Kong), Bregović performed with a string quartet, a male choir, Bulgarian singers and half of a brass band. The other part of the brass band - including bass and percussions - were being played from his computer.

In 1993, Bregović married his long-time girlfriend Dženana Sudžuka. The wedding ceremony held in Paris featured film director Emir Kusturica as the groom's best man and longtime Bijelo Dugme backing vocal, Amila Sulejmanović as the bride's maid of honour.

The couple has three daughters: Ema (born in March 1995), Una (February 2002), and Lulu (May 2004).

Bregović owns real-estate properties all over the world, but spends most of his time between Belgrade, where most of his musical collaborators reside, and Paris, where his spouse lives with their three daughters.

He also has a daughter named Željka (born out of wedlock from a previous relationship) who gave birth to Goran's grand daughter, Bianca. He has a brother named Predrag who lives in New York City, and a sister, Dajana who lives in Split.

On 12 June 2008, Bregović injured his spine, falling from a tree. He fell four meters from a cherry tree in the garden of his home in Senjak, a Belgrade district, breaking vertebrae. However, according to the doctors, his condition was "stable without neurological complications."[8] After surgery, he made a quick recovery and on 8 July and 9 July, he held two big concerts in New York City, where for more than two hours each night, he proved his performance skills had not suffered from the accident.[9]

Bregović prefers to avoid delving into politics. In 2009, he said, "Yugoslavia is the intersection of so many worlds: Orthodox, Catholic, Muslim. With music, I don't have to represent anyone, except myself -- because I speak the first language of the world, the one everyone understands: music."[10] In March 2015, Bregović performed in a concert in Crimea, which was annexed by Russia the previous year. The following month, the Life Festival in Oświęcim, Poland cancelled an appearance by Bregović, saying that his statements were "contrary to the values cherished by the Life Festival founders."[11]